Characterizing Multi-Agent Team Behavior from Partial Team Tracings:Evidence from the English Premier League

Patrick Lucey1, Alina Bialkowski1,2, Peter Carr1, Eric Foote1 and Iain Matthews11Disney Research Pittsburgh, Forbes Avenue, Pittsburgh, PA, 15213

2SAIVT Laboratory, Queensland University of Technology, Brisbane, Australia, QLD, 4001–patrick.lucey,peter.carr,eric.foote,iainm˝@disneyresearch.com

alina.bialkowski@qut.edu.au

AbstractReal-world AI systems have been recently deployedwhich can automatically analyze the plan and tacticsof tennis players. As the game-state is updated reg-ularly at short intervals (i.e. point-level), a library ofsuccessful and unsuccessful plans of a player can belearnt over time. Given the relative strengths and weak-nesses of a player’s plans, a set of proven plans or tac-tics from the library that characterize a player can beidentified. For low-scoring, continuous team sports likesoccer, such analysis for multi-agent teams does notexist as the game is not segmented into “discretized”plays (i.e. plans), making it difficult to obtain a librarythat characterizes a team’s behavior. Additionally, asplayer tracking data is costly and difficult to obtain, weonly have partial team tracings in the form of ball ac-tions which makes this problem even more difficult. Inthis paper, we propose a method to overcome these is-sues by representing team behavior via play-segments,which are spatio-temporal descriptions of ball move-ment over fixed windows of time. Using these repre-sentations we can characterize team behavior from en-tropy maps, which give a measure of predictability ofteam behaviors across the field. We show the efficacyand applicability of our method on the 2010-2011 En-glish Premier League soccer data.

IntroductionThe use of AI systems in sport has graduated from the virtualto the real-world. This is due in part to the popularity of live-sport, the amount of live-sport being broadcasted, the prolif-eration of mobile devices, the rise of second-screen viewing,the amount of data/statistics being generated for sports, anddemand for in-depth reporting and analysis of sport. Sys-tems which use match statistics to automatically generatenarratives have already been deployed (Allen et al. 2010;Statsheet 2012). Although impressive, these solutions justgive a low-level description of match statistics and notableindividual performances without giving any tactical analy-sis about factors which contributed to the result. In tennishowever, IBM has created Slamtracker (IBM SlamTracker2012) which can provide player analysis by finding patternsand styles of play that characterize a player from an enor-mous amount of data.

Copyright c© 2012, Association for the Advancement of ArtificialIntelligence (www.aaai.org). All rights reserved.

(a) (b)

Figure 1: A multi-agent plan recognition (MAPR) frame-work can be used to analyze team tactics of a sporting match.Given a sequence of team behaviors, we can map these toa plan within a library. A set of these common plans canthen describe the underlying tactics employed. For continu-ous and low-scoring sports, such as soccer, segmenting agentbehaviors into a series of plans is difficult. In this paper, weshow a method of circumventing this issue.

Multi-agent plan recognition (MAPR) constitutes amethod to provide this type of analysis for team sports inthe future. Given a sequence of observed team behaviors oractivities, MAPR seeks to map these behaviors to one dis-tinct plan within a library of plans. A set of these recognizedplans can then be used to infer the tactics employed by anagent team in adversarial domains (see Figure 1(a)). As thematch is segmented into distinct plan segments, this typeof approach has started to be applied for team sports suchas American Football (Intille and Bobick 1999; Hess, Fern,and Mortensen 2007; Siddiquie, Yacoob, and Davis 2009;Li and Chellappa 2010; Stracuzzi et al. 2011) and basket-ball (Perse et al. 2008). But due to the difficulty of trackingplayers and the ball in confined spaces, as well as labelingthe complex actions and interactions between players andtheir teammates and adversaries, the large amount of tracingdata which is required to do find characteristic patterns is notavailable. As such, most of the work has been dedicated todoing team activity detection on small amounts of data.

For continuous and low-scoring team sports such as soc-cer, it has the additional headache of the game not being seg-mented into “discretized” plays (i.e. plans) - therefore mak-ing automatic analysis even more difficult. However, due to

Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence

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the explosion in interest in analyzing soccer, there has beena massive demand for real-time statistics and visualizations.Due to the difficulty associated with tracking players andthe ball, most of the data collected is via an army of humanannotators who label all actions that occur around the ball- which they call ball actions. Although only giving partialteam tracing information, the sheer volume of data availablemakes automatic analysis of team behavior an interestingand possible research endeavor.

In this paper, we propose a method to characterize teambehaviors for soccer using partial team tracings. As we donot have a library of labeled plans, we do this by repre-senting team behavior as play-segments, which are spatio-temporal descriptions of ball movement over fixed windowsof time. This differs from current approaches which use la-beled plan libraries and full team tracings (see Figure 1).The ball movements were inferred from the hand annotatedball action dataset which is currently used for visualizationsin sports production (Opta 2012). Using our play-segmentrepresentations we can characterize team behavior from en-tropy maps, which give a measure of predictability of teambehaviors across the field. We show the efficacy and appli-cability of our method on the 2010-2011 English PremierLeague soccer data.

Related WorkMAPR aims to describe the activity sequence of a set ofagents by identifying team structures and behaviors learntfrom a library of team plans (Banerjee, Kraemer, and Lyle2010). Due to the host of military, surveillance and sport ap-plications that it can be utilized in, research into this areahas dramatically increased recently. Outside of the sportrealm, most of this work has focussed on dynamic teams (i.e.where individual agents can leave and join teams over theperiod of the observations). An initial approach to MAPRwas to use a library of single agent plans to recognize teamplans (Avrahami-Zilberbrand et al. 2010). Sukthankar andSycara used a library of team plans but pruned the sizeof the library by using temporal ordering constraints andagent resource dependencies (Sukthankar and Sycara 2008;2012). Banerjee et al.’s work was somewhere in betweenas they “decompressed” the single agent plan library asthey found that it was NP-complete for the multi-agent case(Banerjee, Kraemer, and Lyle 2010). Sadilek and Kautz(Sadilek and Kautz 2008) used GPS locations of multipleagents in a “capture the flag” game to recognize low-levelactivities such as approaching and being at the same loca-tion. All of these works assume that team traces and plansare fully observed, but Zhuo and Li (Laviers et al. 2011) pro-posed a MAX-SAT solver which can do MAPR with partialteam tracings and team plans.

Sport related MAPR research mostly centers on low-levelactivity detection and with the majority centered on Ameri-can Football. In the seminal work by Intille and Bobick (In-tille and Bobick 1999), they recognized a single footballplay pCurl51, using a Bayesian network to model the inter-actions between the players trajectories. Li et al. (Li, Chel-lappa, and Zhou 2009), modeled and classified five offen-sive football plays (e.g. dropback, combo dropback, middle

run, left run, right run). Siddiquie et al. (Siddiquie, Yacoob,and Davis 2009), performed automated experiments to clas-sify seven offensive football plays using a shape (HoG) andmotion (HoF) based spatio-temporal feature. Instead of rec-ognizing football plays, Li and Chellapa (Li and Chellappa2010) used a spatio-temporal driving force model to segmentthe two groups/teams using their trajectories. Researchers atOregon State University have also done substantial researchin the football space (Hess, Fern, and Mortensen 2007;Hess and Fern 2009; Stracuzzi et al. 2011) with the goalof automatically detecting offensive plays from a raw videosource and transfer this knowledge to a simulator. For soc-cer, Kim et al. (Kim et al. 2010) used the global motion ofall players in a soccer match to predict where the play willevolve in the short-term. Beetz et al. (Beetz et al. 2009) de-veloped the automated sport game models (ASPOGAMO)system which can automatically track player and ball posi-tions via a vision system. Using soccer as an example, thesystem was used to gain a heat-map of player positions (i.e.which area of the field did a player mostly spend time in)and also has the capability of clustering passes into low-levelclasses (i.e. long, short etc.), although no thorough analysiswas conducted due to a lack of data. In basketball, Perse etal. (Perse et al. 2008) used trajectories of player movementto recognize three types of team offensive patterns. Hervieuet al. (Hervieu and Bouthemy 2010) also used player trajec-tories to recognize low-level team activities using a hierar-chical parallel semi-Markov model.

Apart from the IBM Slamtracker (IBM SlamTracker2012), no tactical team behavior analysis systems for real-world sports seem to exist. However, this is not the casewith the Robocup domain, especially for the Coach Agentcompetition (Riley and Veloso 2002). “Rush 2008” is a sim-ulation of American Football and was developed as a plat-form for evaluating game-playing agents (Molineaux 2008).Using this simulation, researchers have started to study theproblem of learning strategies by observation (Li et al. 2009)as well as opponent modeling (Laviers et al. 2009).

While similar in spirit, our work differs from these worksmentioned above as we aim to recognize and characterizeteam behaviors for real-world sports, while having no planlibrary, or labels to form a plan library from partial teamtracing data.

Problem FormulationWe define a team as a set of agents having a shared objec-tive and a shared mental state (Cohen and Levesque 1990).As we are dealing with soccer, each agent is permanentlyfixed to one team. Unless an agent has been dismissed fromthe match, each team always has the same number of agents(11). We refer to team behaviors, as short, observable seg-ments of coordinated movement and action executed by ateam (e.g. pass from agent A to agent B). These behaviorsare observed from partial spatio-temporal tracings, whichin this case refers to ball movement inferred from hand-annotated ball-action data (see next section).

A plan can be defined as an ordered sequence of teambehaviors describing a recipe used by a team to achieve agoal (Sukthankar and Sycara 2012). A team performing a

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(a)

(b)

Figure 2: (a) A modified example of the Opta F24 feed be-tween Arsenal and Liverpool. (b) From this we can infer theball position and possession at every time step (solid linesand dots are annotated, dotted lines are inferred).

group of these plans to achieve a major goal (e.g. winninga match), can be said to be employing tactics. However,as soccer is low-scoring, continuous and complex due tothe various multi-agent interactions, labeling and segment-ing the game into a series of plans is extremely difficult.Hence recognizing team tactics using the MAPR frame-work we described previously is impossible without theselabelled plans. To overcome this issue, we quantize a matchinto equal temporal chunks which we use to describe teambehavior. As these segments do not describe a method ofachieving a specific goal, we do not call them plans, butplay-segments. We use these play-segments to form a libraryor playbook of play-segments, P = {p1, p2, p3, . . . , pm},where m is the number of unique play-segments within theplaybook.

The open questions to address with respect to the play-segments are:• How to represent these play-segments given partial team

tracings? Also, what are the optimal parameters of thisrepresentation?

• What tactical insights can we gain from having a play-book of play-segments? Can we devise a visualization orquantitative analysis to back up the analysis?

• How discriminative are our representations? That is, doteams have unique styles of play? And if so, can we detectwhen they deviate from this style?

Using ball action data as our partial tracing data (see nextsection), the rest of the paper is dedicated to answering thesequestions.

Ranking Team Name Ranking Team Name1 Man Utd 11 West Brom2 Chelsea 12 Newcastle3 Man City 13 Stoke City4 Arsenal 14 Bolton5 Tottenham 15 Blackburn6 Liverpool 16 Wigan7 Everton 17 Wolves8 Fulham 18 Birmingham9 Aston Villa 19 Blackpool10 Sunderland 20 West Ham

Table 1: Table showing the team name and ranking for the2010-2011 English Premier League season.

Partial Team Tracing from Ball Action DataDue to the difficulty associated with tracking players and theball, data containing this information is still scarce. Most ofthe data collected is via an army of human annotators wholabel all actions that occur around the ball - which they callball actions. The F24 soccer data feed collected for the En-glish Premier League (EPL) by Opta (Opta 2012) is a goodexample of this. The F24 data is a time coded feed that listsall player action events within the game with a player, team,event type, minute and second for each action. Each eventhas a series of qualifiers describing it. An example of thedata feed is given in Figure 2(a). This type of data is cur-rently used for the real-time online visualizations of events,as well as post-analysis for prominent television and news-paper entities (e.g. ESPN, The Guardian). Even though thisdata has been widely used, there are no systems which usethis data or data like this for automatic tactical analysis.

For our work we used the 2010-2011 EPL season F24Opta feed, which consists of 380 games and more than760,000 events. Each team plays 38 games each, whichcorresponds with each team playing each other team twice(once home and once away). The team names and rankingfor the 2010-2011 EPL data is given in Table 1. In our ap-proach, to analyze the tactics of a team we are required toknow the position of the ball and which team has posses-sion of it at every time step (i.e. every second). To do this,we infer the ball location from the data feed. We describeour method via Figure 2. In (a) we can see at t0 = 114Arsenal successfully passed the ball from (20.2, 64.0) to(35.6, 87.3). As no time is given for the arrival time of thepass, we assume that the pass took one second, so t1 = 115.The next action labeled is that an Arsenal player took ona Liverpool player at (51.2, 84.1), while the Liverpool de-fender unsuccessfully tried to tackle the Arsenal player at(48.8, 15.9) at t4 = 118. As nothing occurred between thetime 115 to 118, we infer that an Arsenal player dribbledthe ball from (35.6, 87.3) to (51.2, 84.1). From these twopoints, we assume that the ball was dribbled in a straightline and at a uniform speed. Based on these assumptions, wecan infer the ball location at t2 = 116 and t3 = 117 and thatArsenal still had possession as the next annotated ball actioninvolved Arsenal having the ball. It is worth noting here thatall data is normalized onto a field of size 100 × 100, withall positions given for teams attacking left to right. So in this

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Figure 3: Given a possession string, we break it up into Nequal chunks and use the quantized ball position values asour play-segment representation, s.

example, even though the take on and tackle occurred at thesame position, the position relative to each team differs. Us-ing the same procedure, we can estimate the ball positionand team possession for the remaining times.

Characterizing Team Behavior via EntropyMaps

Play-Segment RepresentationGiven the observed partial spatio-temporal tracings in agame, O = {A,B}, we partition the tracings for each teaminto possession strings (i.e. continuous movement of theball for a single team without turnover or stoppage), whereA = {a0, . . . ,aI−1} and B = {b0, . . . ,bJ−1} refer to thepossession strings associated with each team and I − 1 andJ − 1 are the number of possessions. We then quantize thefield into a grid of size l × w and vectorize the field via thecolumns. As the possession strings vary in length, we applya sliding window of length T to quantize or chunk the pos-sessions into play-segments S = {s0, . . . , sN−1} of equallength, where N is the total number of play-segments for apossession, and M is the total number of play-segments fora team over a match. Given that a team’s possession string isof length T1, the resulting number of play-segments for eachpossession is therefore: N = (T1−T )+1. If the possessionstring is smaller in duration than T , we discard it. To repre-sent each play-segment p = {p0, . . . , pT−1}, the quantizedball position at each time step is then used to populate eachentry.

A description of this process is given in Figure 3. Giventhe possession string a = {a0, . . . , a13} shown, we firstbreak the field up into a grid of 4 × 5 and then vectorize itto give quantized ball positions. At each time step, the quan-tized ball position is used to populate a. Using T = 10, we

Figure 4: For a set of play-segments which start at a quan-tized field position Si, we can form a probability distribu-tion, p(Si) based on where the ball travels to from this ini-tial position. Using this probability distribution, we can de-termine the entropy of each area which together forms anentropy map.

then chunk a into N = (14 − 10 + 1) = 5 play-segmentsresulting in five play-segments {s0, . . . , s4} shown. Usingthis process, we can get play-segments from all the posses-sion strings to represent a team’s behavior. We used this ap-proach as it allows us to analyze the short-term behavior ofa team over a particular region, which maybe lost otherwise.

Entropy Maps

The entropy or information content of a random dis-crete variable, X with a probability distribution p(X) =(p0, . . . , pn−1) was defined by Shannon (Shannon 1948) as:

H(X) = −n−1∑i=0

p(i) log p(i) (1)

where 0 log∞ = 0 and the base of the logarithm determinesthe unit, (e.g. if base 2 the measure is in bits). Entropy canbe viewed as a measure of uncertainty or how predictable orunpredictable a team’s patterns of play is for different areason the field. For soccer, this means that for each region onthe field we can work out how predictable a team is (e.g. at aparticular region, do teams do the same thing or do they varytheir behavior?). High entropy refers to uncertainty in theinput signal - we need more bits to transfer this information.Low entropy means that the signal is highly predictable -meaning that this information can be transferred by fewerbits.

Using our play-segment representation, we can deter-mine an entropy map to quantify and visualize the pre-dictability of team behavior. We do this as follows: Giventhe observations of a team, we determine the set of play-segments S = {s0, . . . , sN−1}. From these representations,we know where the ball started from and where it travelledover the duration of the play-segment. For each quantizedarea on the field we have a set of play-segments, whereS = {S1, . . . ,Sl×w} and the indices refer to the quantizedfield areas. For each set of play-segments we can then forma probability distribution based on the occupancy for all theplay-segments which started in that quantized area. Fromthis probability distribution we can calculate the entropy forthat area. An example of this procedure is given in Figure 4.

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(a) (b) (c) (d) (e)

Figure 5: Entropy maps which show the characteristic ball movement for (a) Manchester United, (b) Tottenham, (c) StokeCity, (d) Blackburn and (e) Wigan using the entire 38 games for the EPL 2010-2011 season. Note that these maps have beennormalized for teams attacking from left to right.

Mea

nE

ntro

py

Length of Play-Segment Window, T (seconds)

Figure 6: Plot of the mean team entropies for different play-segment windows, T . The order of the curves relating toteam id (see Table 1) are given by the legend on the top ofthe plot (top 10 teams are on the first row, bottom 10 teamsare on the bottom).

Characterizing Teams Using Entropy MapsUsing entropy maps, we can gain both a quantitative as wellas a visual method of seeing how predictable a team is froman area of the field (e.g. are they more dangerous at one areaover another?). For this analysis, we use the entire seasonof data to build a characteristic map of each team. The firstquestion we wanted to answer was “does entropy relate toteam ranking?” and “does this vary depending on T ?”. Todo this we quantized the field into 20 × 16 bins and useddifferent time window lengths to find the entropy map foreach team. The results are shown in Figure 6. As can beseen from this plot, the top five teams have the highest meanentropies for varying play-segment window lengths. Otherthan the top five teams, team ranking does not correspondwith entropy. It is also worth noting that the maximum en-tropy occurs around 4 to 5 seconds for all teams, which isimportant to note as this also means that this window of timemaximizes the amount of information available. It might betempting however to use a longer window as there is greaterseparation in the curves, but this also relates to a drop off ininformation which reduces the discriminative power of thesignal.

In Figure 5, we show the characteristic entropy mapsof five teams, (a) Manchester United (rank 1), (b) Totten-ham (rank 5), Stoke City (rank 13), Blackburn (rank15) andWigan (rank 16). As T = 5 yields the most information,

we used this time window for the rest of experiments (i.e.heuristically, we found this to be the case as well). Gener-ally, it can be seen that the the entropy around goal area inthe attacking end is low due to the amount of players that arearound these areas trying to protect the goal as well as thecorners which makes sense as there are relatively little op-tions from these positions. More specifically, in (a) and (b),the heavy redness throughout the maps is evident, especiallythrough the centers which signifies both Manchester Unitedand Tottenham are passing teams who move the ball aroundquite well. The heavy red for Manchester United is morepronounced on the right-side of the field (relative to eachteam attacking left-to-right on the page), while for Totten-ham it is on the left. These trends make sense as ManchesterUnited have Luis Nani who is a dynamic winger who tendsto spend a lot of time in these areas, and Tottenham haveGareth Bale who has similar traits on the left-hand side. Innext two maps (c) and (d), it is apparent that both these teamsdo not play such an expansive passing game, which makessense as both Stoke City and Blackburn play a predicable di-rect style (i.e. from the back they kick the ball long to theirforwards to minimize the amount of error in their defensivehalf). In the last map (e), we see that despite finishing in16th position, Wigan played a similar style to the top teams,although it can be seen that they do not utilize the width asmuch.

Identifying Team Behavior VariationIn terms of tactical analysis at the match level, it is importantto be able to determine what type of style a team is play-ing. Additionally, it is important to see if they are playingas expected or they have employed a new style of play. Todo this, we conducted some team identification experiments.Not only do these experiments allow us to determine thesethings, we also get to see how discriminative our represen-tations are, as well as seeing if individual teams have uniquestyles of play. The team identification task we posed was,given we have the play-segment playbooks for a home andaway team, could we correctly identify the home team? Forthese experiments, we used the entire 380 games of the sea-son and used a leave-one-match-out cross validation strat-egy to maximize training and testing data. To show how dis-criminative our entropy map approach was, we comparedit to twenty-three match statistics currently used in analysis(e.g. passes, shots, tackles, fouls, aerials, possession, time-in-play etc.), as well as a combination of the entropy mapand match statistics. For classification, we used a k-NearestNeighbor approach. All experiments were conducted using

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Figure 7: Confusion matrices for the team identification experiments using: (a) match statistics (accuracy = 19%), (b) entropymaps (accuracy = 30%), (c) concatenation of match statistics and entropy map (accuracy = 47%). The actual team identity isgiven on the vertical axis, while the predicted/recognized identity is given on the horizontal axis. Also, notice that in (c) theteam that got ranked (1) got confused as the last placed team for a game (red circle in the top right corner).

a play-segments size of 10 × 8 over a window of T = 5 aswe heuristically we found this to yield optimal results. Allfeature sets were also scaled and underwent a step of LDA(linear discriminant analysis) to gain a compact, class pre-serving representation. The confusion matrices for the threedifferent feature sets are given in Figure 7.

As can be seen from the first confusion matrix (a),very little discriminative information about the team ex-ists with accuracy of about 19% obtained (chance is 5%).The entropy maps reached 30% accuracy, with the diago-nal clearly visible. Combining both information sources to-gether greatly improves the classification accuracy again,with 47% achieved, which is very good when you considerwe only have the ball movement data. It also shows thatteams do have unique styles of play which can be pickedup from using our approach. It is also worth noting that theteams that tend to get confused with each other play similarstyles. An example of this is teams 13, 14, 15 (Stoke, Boltonand Blackburn). As mentioned previously, these teams tendto play a very similar simple and predicable direct style. Thisplot shows that they do not vary this style much during theseason, which also reinforces why their entropy levels werethe lowest out of all the teams (see Figure 6. These alsoseems to be a trend for the top teams, where they often getconfused with each other which means they also play similarstyles. But this begs the question, when they play each otherdo they play the same style or do they play another style? Toanswer this, we can use this team identification result shownin the top corner of Figure 6(c).

When looking at the result, the top team ManchesterUnited got confused with the bottom team West HamUnited. Their opponent on this occasion was Arsenal whofinished fourth and play a very expansive passing game,which is highlighted by the fact that they have the highestentropy value. When we compare the mean entropy mapof Manchester United to their entropy map of the game inFigure 8 (a) and (b) we can see the difference. When youcompare this to the West Ham mean entropy map, you cansee why it got confused. What is interesting to note though,

(a) (b) (c)

Figure 8: Entropy maps for (a) Average Man Utd perfor-mance, (b) Man Utd performance vs Arsenal, (c) AverageWest Ham performance. Our analysis shows that for thisgame, Man Utd’s style changed to a more counter-attackingWest Ham style.

is that on this occasion Manchester United actually won 2-0 by playing a counter attacking game (e.g. be defensivelycompact and break quickly). Due to a relative lack of talent,West Ham played this style too but probably did not have theoffensive weapons to pull this off. A tactical analysis of thisgame is given by zonalmarking.net (Zonalmarking 2011).

Summary and Future WorkIn this paper, we proposed a method to characterize teambehavior for soccer by representing team behavior via play-segments, which are spatio-temporal descriptions of ballmovement over fixed windows of time. Using these rep-resentations we characterized team behavior from entropymaps, which gives a measure of predictability of team be-haviors across the field. As soccer is low-scoring and con-tinuous, analyzing team patterns of play is difficult as thereis no library of labeled plan or full team tracings, which dif-fers from current MAPR approaches which use labeled planlibraries and full team tracings. We illustrated the benefit ofour approach on the 2010-2011 English Premier League soc-cer data by characterizing teams via entropy maps, as well asshowing how our approach can be used to detect team stylevariation through team identification experiments. In the fu-ture we endeavor to use this type of approach to characterizeteam behaviors in goal-scoring scenarios. Also, seeing thatwe can do this type of analysis using partial team tracingswe plan to develop this tool on a tablet device, such as aniPad which would make it accessible in amateur and semi-professional sporting domains.

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